Fractional Diffusion Equations Solved via Log–Laplace Residual Power Series
DOI:
https://doi.org/10.31185/wjps.973Keywords:
Caputo-Hadamard, Residual Power Series, Log(t+1)- Laplace, Diffusion EquationAbstract
In this paper, fractional diffusion equations of Caputo-Hadamard presented as interesting classes of fractional differential equations have not studied before. For the first time, the solution to a diffusion equation of this type was calculated. Therefore, it is considered a new addition to the diffusion equation with the presence of this form of fractional derivatives, with its initial conditions. Additionally, this paper presents a suitable Laplace logarithmic formula for the given fractional equation, derived from the generalized Laplace formula and its established conditions. This also relies on the formula for the fractional derivative as a transformation. The first time this type of fractional derivative was established, it helped in finding an approximate formula for the solution. The residual power series method used is effective in solving many fractional equations and was even more effective when used with the Laplace logarithmic formula. The Log(t+1) –Laplace residual power series method combines the two concepts, formulating and evaluating the method, shown that from any changing of the values of the parameters involving in formulation of derivative as well as the values of fractional order which found in tables and figures for illustrative examples which illustrates the presented method.
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